Matt Damon, Bill Murray, John Goodman and George Clooney promote their new movie The Monuments Men. Photograph: Dave M. Benett/WireImage

Part of the Athens marbles, taken by Elgin. Photograph: PjrTravel/Alamy

They came to promote a film showing how millions of artworks were rescued and returned to their rightful owners after plunder by the Nazis. But George Clooney, Bill Murray and Matt Damon left implying that Britain, too, needed to have a long, hard, look at itself.

The Hollywood actors had become embroiled in one of the fiercest of all heritage controversies: should the Elgin marbles, removed from the Parthenon 200 years ago, be housed in London or in Athens?

At the National Gallery, Clooney repeated his belief that it would be a good thing if the British Museum gave the 2,500-year-old sculptures back to Greece. He was backed by Murray, who said they had had "a very nice stay here" but now should be returned.

The actors joined a dispute which has simmered ever since enormous chunks of the Parthenon's statuary were removed by Lord Elgin, British ambassador to the Ottoman empire, in the early 19th century.

Later bankrupt, Elgin sold them to the British government for £35,000 and they made their way to the British Museum, where they have remained a star attraction ever since.

Matt Damon, Bill Murray, John Goodman and George Clooney promote their new movie The Monuments Men. Photograph: Dave M. Benett/WireImage

In London on Tuesday, the question was put to him again. "I did a little research just to make sure I wasn't completely out of my mind," he said.

Slipping on pronunciation, he added: "Even in England the polling is in favour of returning the marbles from the Pantheon [sic], the Pantheon marbles."

Clooney said the Vatican and the Getty museum, in Los Angeles, had returned parts of the Parthenon and suggested the question was whether a piece of broken-up art should be put back together as best as possible. In this case returning them was "probably the right thing to do".

The actor said it was suggested over the weekend that because he was an American he probably didn't understand. "That's probably right," he deadpanned.

But Damon quickly chipped in: "That can't always be the British default position. I mean seriously, it's not actually an argument to say we are Americans we don't get it."

Clooney added: "I do think it's worth having an open discussion." But he suggested he might not be getting his placards out quite yet.

"It was one of a hundred questions at a press conference, a Greek reporter asking me about the marbles – and I just said I thought it was probably a good idea if they found a way back at some point."

His view was backed though by Murray, who plays one of the Monuments Men.

Murray said: "It seems like it's a problem all over the world. Who owns this art? Where it came from? Do they have the right to give it back? I think it has had a very nice stay here, certainly. London's gotten crowded, there's plenty of room back there in Greece, plenty of room. England can take a lead on this kind of thing … letting art go back where it came from.

"If [the marbles] were all together the Greeks are nothing but generous – they'd loan it back every once in a while … like people do with art."

Would Clooney visit the British Museum to look at the marbles? The problem was time, he said, as they were due to leave for Paris that evening "to somehow insult the Parisians, something about the Mona Lisa and Italy".

In Greece, reaction to Clooney's unexpected support was as swift as it was effusive. With the return of "Elgin's loot" the single biggest priority on the arts agenda of the tourist-reliant country, the culture minister, Panos Panagiotopoulos, penned a two-page letter to the actor expressing the "heartfelt thanks of all Greeks" for his solidarity.

He wrote: "As you said, returning these pillaged masterpieces to where they belong on the Parthenon would be both fair and nice … not only because they belong to the history of Greek civilisation, but precisely because through our history they illuminate world civilisation."

There was, he continued, only one decision that could right the wrong. "The decision to return the marbles to the place where they were chiselled, next to those sculptures from which they were so illegally and violently ripped apart."

But at the British Museum there was little sign of policy change. A spokeswoman said everyone was entitled to their view. "The trustees have always been very clear on the benefits of [their]remaining at the museum where they can be seen as part of a world collection. The purpose of the British Museum is to present the world to the world."

She said the issue was much more complicated than often thought and there was "a danger of oversimplifying the issue". Nor is Clooney likely to alter UK political policy. The government supports the British Museum, and the shadow culture minister, Helen Goodman, said the museum had looked after the marbles brilliantly. "How would George Clooney feel if he could only act in American films shown in the US?"

Pillage or protection?

Of the sculptures that once adorned the Parthenon about half had been lost or destroyed by the time Lord Elgin's agents began removing chunks between 1800 and 1805.

It is these statues, once known as the Elgin marbles now as the Parthenon marbles, that have caused bitter controversy for 200 years.

Elgin was British ambassador to the Ottoman empire, of which Athens had been a part for 350 years. His fans argue that he took the marbles with permission and with the best of intentions – that he was passionate about saving Greek art.

Others see the removal of boatloads of ancient art by Elgin's agents as an act of pillage. Lord Byron took on Elgin in verse – "Dull is the eye that will not weep to see / Thy walls defaced, thy mouldering shrines removed / By British hands".

That was not a universally held sentiment. Keats wrote a poem in celebration of seeing the sculptures, and Goethe called their acquisition "the beginning of a new age for Great Art".

The museum has about half of the remaining marbles; Athens having got the others, although fragments exist in collections such as the Louvre. In 2009, before the crash, Greece opened its New Acropolis Museum and says it could hold the marbles. The British Museum is adamant they're fine where they are – part of a collection which shows the world.